The task of Structural Health Monitoring (SHM) of aging highway bridges and overpasses is important not only from the point of preventing economic losses from traffic delays and detours but also is a matter of preventing catastrophic failures and loss of human life. In recent years, wireless sensor technologies have been used extensively to develop SHM platforms for bridges. A limitation of wireless sensors is the finite life span of batteries and high cost of battery replacements which make such systems prohibitively expensive in many cases. Energy harvesting is a solution capable to alleviate this problem. A novel wireless sensor system is presented that harvests vibrations of the bridge created by passing traffic which is converted into usable electrical energy by means of a linear electromagnetic generator. Utilization of an electromagnetic generator allows harvesting of up to 12.5mW of power in the resonant mode with the frequency of excitation at 3.1Hz, in this particular design. The novelty of the system also includes tight integration of the power generator and a smart algorithm for energy conversion that switches between the low-power mode and the impedance matching mode. Finally, results of field experiments are presented in which the wireless system is operated exclusively by the harvested energy of vibration on a rural highway bridge with low traffic volume.